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Article #2359Re: Trig. inequality
From: David Karr
Date: Sun, 22 Nov 1992 05:04
Date: Sun, 22 Nov 1992 05:04
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1120 bytes
In article <1992Nov22.030801.4773@dartvax.dartmouth.edu> J.Theodore.Schuerzinger@dartmouth.edu (J. Theodore Schuerzinger) writes: >In article <1ekddfINNi96@uwm.edu> >radcliff@csd4.csd.uwm.edu (David G Radcliffe) writes: > >> Show that (sin x)^(sin x) < (cos x)^(cos x) when 0 < x < pi/4. > >[...] (cos x)^2 will be greater than (sin x)^2 from 0<x<pi/4. I >haven't taken any math since freshman year of college, [...] We could have figured the last part out ourselves. :-) The problem is you DON'T have (sin x)^2 on the left, you have (sin x)^(sin x), which is considerably bigger. The behavior of this object as x->0 is not as obvious as that of any fixed power of sin(x). -- David Karr (karr@cs.cornell.edu)
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Newsgroups: rec.puzzles Path: arc1-ca.pugleaf.net!sparky!uunet!usc!rpi!batcomputer!cornell!karr From: karr@cs.cornell.edu (David Karr) Subject: Re: Trig. inequality Message-ID: <1992Nov22.050428.28191@cs.cornell.edu> Organization: Cornell Univ. CS Dept, Ithaca NY 14853 References: <1ekddfINNi96@uwm.edu> <1992Nov22.030801.4773@dartvax.dartmouth.edu> Date: Sun, 22 Nov 1992 05:04:28 GMT Lines: 20